(C₂×#261)⋊C₄ #88114

order	416
isoclinism	isoclinic class of #6118
automorphism	?
homology	Abelianization (H₁) = C₄² · Schur multiplier (H₂) = C₂³

Aliases

Fitting	C₂×C₄×C₁₃ ⋊ C₄
Sylow	C₁₃ ⋊ #95

76 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 104

A minimal faithful permutation representation — 2 generators on 21 points:

(1,2,5,8,12,6,10,11,3,7,13,9,4)(14,15,16,17)(19,21);(2,3,4,6)(5,8,9,13)(7,11,12,10)(18,19)(20,21)

Polycyclic presentation:

2^5,13|a^2=c,b^2=d,b^a=be,f^a=f^8,f^c=f^12

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(416, 81);